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First operation: 3L-1L=2=6/3L of wine left, total 4L;#2: 6/3L-(6/3)/4=6/3-6/12=18/12=6/4L of wine left, total 5L;#3: 6/4L-(6/4)/5=6/4-6/20=24/20=6/5L, total 6L;#4: 6/5L-(6/5)/6=6/5-6/30=30/30=6/6L, total 7L;....

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25 Sep 2010, 11:08

Bunuel wrote:

Let's go step by step:

First operation: 3L-1L=2=6/3L of wine left, total 4L;#2: 6/3L-(6/3)/4=6/3-6/12=18/12=6/4L of wine left, total 5L;#3: 6/4L-(6/4)/5=6/4-6/20=24/20=6/5L, total 6L;#4: 6/5L-(6/5)/6=6/5-6/30=30/30=6/6L, total 7L;....

At this point it's already possible to see the pattern: x=6/(n+2)

n=19 --> x=6/(19+2)=6/21=2/7L

Answer: A.

Bunuel could you please explain the calculation for the 2nd op... Thanks

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First operation: 3L-1L=2=6/3L of wine left, total 4L;#2: 6/3L-(6/3)/4=6/3-6/12=18/12=6/4L of wine left, total 5L;#3: 6/4L-(6/4)/5=6/4-6/20=24/20=6/5L, total 6L;#4: 6/5L-(6/5)/6=6/5-6/30=30/30=6/6L, total 7L;....

At this point it's already possible to see the pattern: x=6/(n+2)

n=19 --> x=6/(19+2)=6/21=2/7L

Answer: A.

Bunuel could you please explain the calculation for the 2nd op... Thanks

After 1st operation 2=6/3L of wine is left out of total 4L. When then for 2nd operation we remove 1L of mixture (or 1/4th of total mixture), we remove 2*1/4 of wine as well.

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26 Jan 2011, 15:46

Bunuel wrote:

Let's go step by step:

First operation: 3L-1L=2=6/3L of wine left, total 4L;#2: 6/3L-(6/3)/4=6/3-6/12=18/12=6/4L of wine left, total 5L;#3: 6/4L-(6/4)/5=6/4-6/20=24/20=6/5L, total 6L;#4: 6/5L-(6/5)/6=6/5-6/30=30/30=6/6L, total 7L;....

At this point it's already possible to see the pattern: x=6/(n+2)

n=19 --> x=6/(19+2)=6/21=2/7L

Answer: A.

I don't understand how the sequence could result in 2/7.

6/3 is supposed to be the ratio of 2

The first sequence begins by 3L-1L= 2L then 2L+2L=4L the process goes on until it becomes 21L because the process is like simply adding one over and over again.

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First operation: 3L-1L=2=6/3L of wine left, total 4L;#2: 6/3L-(6/3)/4=6/3-6/12=18/12=6/4L of wine left, total 5L;#3: 6/4L-(6/4)/5=6/4-6/20=24/20=6/5L, total 6L;#4: 6/5L-(6/5)/6=6/5-6/30=30/30=6/6L, total 7L;....

At this point it's already possible to see the pattern: x=6/(n+2)

n=19 --> x=6/(19+2)=6/21=2/7L

Answer: A.

I don't understand how the sequence could result in 2/7.

6/3 is supposed to be the ratio of 2

The first sequence begins by 3L-1L= 2L then 2L+2L=4L the process goes on until it becomes 21L because the process is like simply adding one over and over again.

I'm really confused please help me!

After the first operation there will be 2L of wine left. 2 can be expressed as a fraction and be written as 6/3. Then as you can see in the solution, for any operation the amount of wine can be expressed as 6/(# of operations+2) L.

Anyway: this is not a GMAT question, so don't worry about it._________________

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26 Jan 2011, 16:36

Bunuel wrote:

mariyea wrote:

Bunuel wrote:

Let's go step by step:

First operation: 3L-1L=2=6/3L of wine left, total 4L;#2: 6/3L-(6/3)/4=6/3-6/12=18/12=6/4L of wine left, total 5L;#3: 6/4L-(6/4)/5=6/4-6/20=24/20=6/5L, total 6L;#4: 6/5L-(6/5)/6=6/5-6/30=30/30=6/6L, total 7L;....

At this point it's already possible to see the pattern: x=6/(n+2)

n=19 --> x=6/(19+2)=6/21=2/7L

Answer: A.

I don't understand how the sequence could result in 2/7.

6/3 is supposed to be the ratio of 2

The first sequence begins by 3L-1L= 2L then 2L+2L=4L the process goes on until it becomes 21L because the process is like simply adding one over and over again.

I'm really confused please help me!

After the first operation there will be 2L of wine left. 2 can be expressed as a fraction and be written as 6/3. Then as you can see in the solution, for any operation the amount of wine can be expressed as 6/(# of operations+2) L.

Anyway: this is not a GMAT question, so don't worry about it.

Thank you for taking the time anyway. It's good to understand solutions to difficult problems b/c it makes future problems easier to tackle. _________________

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bc every time we take out 1 liter of mixture and add 2 liters of water. how is *3/5*4/6****calculate that?

thanks a lot.

First time, \(C_f = 1 * 2/4\)Second time when you remove 1 litre from 4 litres, Initial Volume becomes 3 lts. When you add 2 lts of water back, final volume becomes 5 lts.

Now for second step, \(C_f = C_i * 3/5\)\(C_i\) for the second step is the final concentration obtained from step 1 i.e. \(C_i\) for second step = 1 * 2/4So, \(C_f = 1 * 2/4 * 3/5\)and so on for every subsequent step... It doesn't matter whether we have 19 or 119 steps, we still get our answer in 2 steps.
_________________